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This paper presents techniques of maximum power point tracking (MPPT) implemented with finite step model predictive control (FSMPC) for the application of Z-source inverter. Incremental conductance MPPT algorithm and FSMPC model is developed to control the output current of the grid-tied Z-source inverter in order to extract maximum solar power from the panel and then directly injecting the power into grid. The output current, passive component voltage and current are well regulated with proposed MPPT based FSMPC control strategy. Simulation of this proposed control algorithm is conducted in Matlab platform with PLECS toolbox. Both steady-state and transient results show that the high efficient and robust response of the proposed control technique.